Steve Haddock remembers every detail about his first ocean encounter with a comb jelly. The open water was a bottomless deep blue. The animal, about the size of a tennis ball, shimmered with bioluminescence. “It was just cruising along like a hover craft,” says Haddock, a marine biologist at Monterey Bay Aquarium Research Institute in Moss Landing, Calif. “Comb jellies are more alien than any aliens people imagine,” he says.

Start with their appearance: The marine animals resemble translucent ...